J P Mohindru and Bharat Mohindru Solutions for Chapter: Arithmetic Progressions, Exercise 4: EXERCISE

If the $5^{\mathrm{th}}$ and ${12}^{\mathrm{th}}$ terms of an A.P. are $30$ and $65$ respectively, then what is the sum of the first $20$ terms?

If the sum of first $p$ terms of an A.P. is equal to the sum of first $q$ terms, then find the sum of the first $\left(p+q\right)$ terms.

The sum of $n$ terms of two arithmetic progressions are in the ratio $\left(3n+8\right):\left(7n+15\right)$. Find the ratio of their ${12}^{\mathrm{th}}$ terms. 

A gentleman buys bank's certificates of value exceeding the last year's purchase by $₹25$ every year. After $20$ years, he finds that the value of the certificates purchased by him is $₹7250$. Find the value of the certificates bought by him in the first year.

A gentleman buys every year Bank's certificates of value exceeding the last year's purchase by $₹25$. After $20$ years he finds that the value of the certificates purchased by him is $₹7250$. Find the value of the certificates bought by him in the $13\mathrm{th}$ year.

If in an A.P., $S_1=6$ and $S_7=105$, prove that: $S_n:S_{n-3}::\left(n+3\right):\left(n-3\right)$. 

If in an A.P., $S_3=6$ and $S_6=3$, prove that: $2\left(2n+1\right)S_{n+4}=\left(n+4\right)S_{2n+1}$.

If $S_1,S_2,S_3$ be the sum of $n,2n,3n$ terms respectively of an A.P., prove that $S_3=3\left(S_2-S_1\right)$.